The authors have declared that no competing interests exist.

In this study, the ground state energies of face-centered cubic Hubbard clusters are analyzed using the Lanczos method. Examination of the ground state energy as a function of the number of particle per site

The Hubbard model [_{B}). This behavior shows a significant itinerancy of _{i,σ}) is the fermionic operator which creates (destroys) an electron with spin _{i,↑} is the particle number operator at site

Despite the simplicity of the model, full exact solutions in the thermodynamic limit have been obtained only for the one-dimensional structures [

Finding solutions for higher dimensions remains a challenging task and many approaches have been put forward to study specific features and interaction scenarios using the Hubbard model including the mean-field approximation, perturbation theory, and dynamical mean-field approximation (DMFA). A more convenient approach relies on dealing with the model outside the thermodynamic limit, where it is possible to apply computational techniques such as exact diagonalization and quantum Monte Carlo (QMC) methods, which are discussed in this paper.

The electronic correlations among electrons present in the 3_{B}. This magnetic moment represents itinerant particles density, which in this case are roles rather than electrons [

Several works have used the single-band Hubbard model [_{s}), around 4–6, were considered because of computing limitations at that time. In this work, we were able to study 8–12 sites using new computer configurations and optimized Lanczos algorithm.

A set of orthogonal basis vectors was constructed for the Hamiltonian [_{0}〉, from which a set of orthogonal vectors was spanned following the rule

The numerical instabilities in some systems require other approaches to the Lanczos method [

We initially determined the ground-state energy and total spin as a function of the coulombic interaction for the

The ground-state energy per site as a function of the particle density was then evaluated above the transition point (with the system in the ferromagnetic state) for _{s} = 8, 9, 10, 11 and 12. When _{s}.

The solid lines are guides for the eye.

Slightly above the transition point at _{s}. The increase in the

The number of sites _{s} varies from 8 to 12. The solid lines are guides for the eye.

We analyzed the electronic correlations in the fcc clusters using the single-band Hubbard model for several coulombic interaction regimes defined by

These results reinforce the analysis reported by Macedo and Souza [

When considering the properties of Ni, the

This work was supported by CAPES (Brazilian Agency). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. We thank G. M. A. Almeida for the careful reading of the manuscript.